Mercurial > repos > public > sbplib

annotate +sbp/+implementations/d4_6.m @ 1347:ac54767ae1fb feature/poroelastic tip

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
Add interface, not fully compatible.
author Martin Almquist <martin.almquist@it.uu.se>
date Tue, 30 Apr 2024 14:58:35 +0200
parents f7ac3cd6eeaa
children
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
261
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
1 function [H, HI, D1, D2, D3, D4, e_1, e_m, M, M4,Q, Q3,...
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
2 S2_1, S2_m, S3_1, S3_m, S_1, S_m] = d4_6(m,h)
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
3 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
4 %%% 4:de ordn. SBP Finita differens %%%
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
5 %%% operatorer framtagna av Ken Mattsson %%%
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
6 %%% %%%
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
7 %%% 6 randpunkter, diagonal norm %%%
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
8 %%% %%%
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
9 %%% Datum: 2013-11-11 %%%
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
10 %%% %%%
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
11 %%% %%%
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
12 %%% H (Normen) %%%
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
13 %%% D1 (approx f?rsta derivatan) %%%
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
14 %%% D2 (approx andra derivatan) %%%
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
15 %%% D3 (approx tredje derivatan) %%%
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
16 %%% D2 (approx fj?rde derivatan) %%%
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
17 %%% %%%
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
18 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
19
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
20 % M?ste ange antal punkter (m) och stegl?ngd (h)
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
21 % Notera att dessa opetratorer ?r framtagna f?r att anv?ndas n?r
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
22 % vi har 3de och 4de derivator i v?r PDE
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
23 % I annat fall anv?nd de "traditionella" som har noggrannare
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
24 % randsplutningar f?r D1 och D2
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
25
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
26 % Vi b?rjar med normen. Notera att alla SBP operatorer delar samma norm,
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
27 % vilket ?r n?dv?ndigt f?r stabilitet
266
bfa130b7abf6 Added error message for too few grid points to all implementation files.
Martin Almquist <martin.almquist@it.uu.se>
parents: 261
diff changeset
28
bfa130b7abf6 Added error message for too few grid points to all implementation files.
Martin Almquist <martin.almquist@it.uu.se>
parents: 261
diff changeset
29 BP = 8;
bfa130b7abf6 Added error message for too few grid points to all implementation files.
Martin Almquist <martin.almquist@it.uu.se>
parents: 261
diff changeset
30 if(m<2*BP)
bfa130b7abf6 Added error message for too few grid points to all implementation files.
Martin Almquist <martin.almquist@it.uu.se>
parents: 261
diff changeset
31 error(['Operator requires at least ' num2str(2*BP) ' grid points']);
bfa130b7abf6 Added error message for too few grid points to all implementation files.
Martin Almquist <martin.almquist@it.uu.se>
parents: 261
diff changeset
32 end
261
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
33
267
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
34 H=speye(m,m);
261
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
35 H_U=[0.318365e6 / 0.1016064e7 0 0 0 0 0 0 0; 0 0.145979e6 / 0.103680e6 0 0 0 0 0 0; 0 0 0.139177e6 / 0.241920e6 0 0 0 0 0; 0 0 0 0.964969e6 / 0.725760e6 0 0 0 0; 0 0 0 0 0.593477e6 / 0.725760e6 0 0 0; 0 0 0 0 0 0.52009e5 / 0.48384e5 0 0; 0 0 0 0 0 0 0.141893e6 / 0.145152e6 0; 0 0 0 0 0 0 0 0.1019713e7 / 0.1016064e7;];
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
36
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
37 H(1:8,1:8)=H_U;
267
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
38 H(m-7:m,m-7:m)=rot90(H_U,2);
261
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
39 H=H*h;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
40 HI=inv(H);
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
41
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
42
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
43 % First derivative SBP operator, 1st order accurate at first 6 boundary points
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
44
267
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
45 % q3=1/60;q2=-3/20;q1=3/4;
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
46 % Q=q3*(diag(ones(m-3,1),3) - diag(ones(m-3,1),-3))+q2*(diag(ones(m-2,1),2) - diag(ones(m-2,1),-2))+q1*(diag(ones(m-1,1),1)-diag(ones(m-1,1),-1));
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
47 diags = -3:3;
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
48 stencil = [-1/60,3/20,-3/4,0,3/4,-3/20,1/60];
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
49 Q = stripeMatrix(stencil, diags, m);
261
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
50
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
51 Q_U = [0 0.1547358409e10 / 0.2421619200e10 -0.422423e6 / 0.11211200e8 -0.1002751721e10 / 0.8717829120e10 -0.15605263e8 / 0.484323840e9 0.1023865e7 / 0.24216192e8 0.291943739e9 / 0.21794572800e11 -0.24659e5 / 0.2534400e7; -0.1547358409e10 / 0.2421619200e10 0 0.23031829e8 / 0.62899200e8 0.10784027e8 / 0.34594560e8 0.2859215e7 / 0.31135104e8 -0.45982103e8 / 0.345945600e9 -0.26681e5 / 0.1182720e7 0.538846039e9 / 0.21794572800e11; 0.422423e6 / 0.11211200e8 -0.23031829e8 / 0.62899200e8 0 0.28368209e8 / 0.69189120e8 -0.9693137e7 / 0.69189120e8 0.1289363e7 / 0.17740800e8 -0.39181e5 / 0.5491200e7 -0.168647e6 / 0.24216192e8; 0.1002751721e10 / 0.8717829120e10 -0.10784027e8 / 0.34594560e8 -0.28368209e8 / 0.69189120e8 0 0.5833151e7 / 0.10644480e8 0.4353179e7 / 0.69189120e8 0.2462459e7 / 0.155675520e9 -0.215471e6 / 0.10762752e8; 0.15605263e8 / 0.484323840e9 -0.2859215e7 / 0.31135104e8 0.9693137e7 / 0.69189120e8 -0.5833151e7 / 0.10644480e8 0 0.7521509e7 / 0.13837824e8 -0.1013231e7 / 0.11531520e8 0.103152839e9 / 0.8717829120e10; -0.1023865e7 / 0.24216192e8 0.45982103e8 / 0.345945600e9 -0.1289363e7 / 0.17740800e8 -0.4353179e7 / 0.69189120e8 -0.7521509e7 / 0.13837824e8 0 0.67795697e8 / 0.98841600e8 -0.17263733e8 / 0.151351200e9; -0.291943739e9 / 0.21794572800e11 0.26681e5 / 0.1182720e7 0.39181e5 / 0.5491200e7 -0.2462459e7 / 0.155675520e9 0.1013231e7 / 0.11531520e8 -0.67795697e8 / 0.98841600e8 0 0.1769933569e10 / 0.2421619200e10; 0.24659e5 / 0.2534400e7 -0.538846039e9 / 0.21794572800e11 0.168647e6 / 0.24216192e8 0.215471e6 / 0.10762752e8 -0.103152839e9 / 0.8717829120e10 0.17263733e8 / 0.151351200e9 -0.1769933569e10 / 0.2421619200e10 0;];
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
52
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
53 Q(1:8,1:8)=Q_U;
267
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
54 Q(m-7:m,m-7:m)=rot90( -Q_U ,2 );
261
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
55
267
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
56 e_1=sparse(m,1);e_1(1)=1;
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
57 e_m=sparse(m,1);e_m(m)=1;
261
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
58
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
59
267
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
60 D1=H\(Q-1/2*(e_1*e_1')+1/2*(e_m*e_m')) ;
261
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
61
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
62 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
63
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
64
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
65
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
66 % Second derivative, 1st order accurate at first 6 boundary points
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
67 m3=-1/90;m2=3/20;m1=-3/2;m0=49/18;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
68
267
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
69 % M=m3*(diag(ones(m-3,1),3)+diag(ones(m-3,1),-3))+m2*(diag(ones(m-2,1),2)+diag(ones(m-2,1),-2))+m1*(diag(ones(m-1,1),1)+diag(ones(m-1,1),-1))+m0*diag(ones(m,1),0);
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
70 diags = -3:3;
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
71 stencil = [m3,m2,m1,m0,m1,m2,m3];
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
72 M = stripeMatrix(stencil, diags, m);
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
73
261
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
74 M_U=[0.4347276223e10 / 0.3736212480e10 -0.1534657609e10 / 0.1210809600e10 0.68879e5 / 0.3057600e7 0.1092927401e10 / 0.13076743680e11 0.18145423e8 / 0.968647680e9 -0.1143817e7 / 0.60540480e8 -0.355447739e9 / 0.65383718400e11 0.56081e5 / 0.16473600e8; -0.1534657609e10 / 0.1210809600e10 0.42416226217e11 / 0.18681062400e11 -0.228654119e9 / 0.345945600e9 -0.12245627e8 / 0.34594560e8 -0.2995295e7 / 0.46702656e8 0.52836503e8 / 0.691891200e9 0.119351e6 / 0.12812800e8 -0.634102039e9 / 0.65383718400e11; 0.68879e5 / 0.3057600e7 -0.228654119e9 / 0.345945600e9 0.5399287e7 / 0.4193280e7 -0.24739409e8 / 0.34594560e8 0.7878737e7 / 0.69189120e8 -0.1917829e7 / 0.31449600e8 0.39727e5 / 0.3660800e7 0.10259e5 / 0.4656960e7; 0.1092927401e10 / 0.13076743680e11 -0.12245627e8 / 0.34594560e8 -0.24739409e8 / 0.34594560e8 0.7780367599e10 / 0.3736212480e10 -0.70085363e8 / 0.69189120e8 -0.500209e6 / 0.6289920e7 -0.311543e6 / 0.17962560e8 0.278191e6 / 0.21525504e8; 0.18145423e8 / 0.968647680e9 -0.2995295e7 / 0.46702656e8 0.7878737e7 / 0.69189120e8 -0.70085363e8 / 0.69189120e8 0.7116321131e10 / 0.3736212480e10 -0.545081e6 / 0.532224e6 0.811631e6 / 0.11531520e8 -0.84101639e8 / 0.13076743680e11; -0.1143817e7 / 0.60540480e8 0.52836503e8 / 0.691891200e9 -0.1917829e7 / 0.31449600e8 -0.500209e6 / 0.6289920e7 -0.545081e6 / 0.532224e6 0.324760747e9 / 0.138378240e9 -0.65995697e8 / 0.49420800e8 0.1469203e7 / 0.13759200e8; -0.355447739e9 / 0.65383718400e11 0.119351e6 / 0.12812800e8 0.39727e5 / 0.3660800e7 -0.311543e6 / 0.17962560e8 0.811631e6 / 0.11531520e8 -0.65995697e8 / 0.49420800e8 0.48284442317e11 / 0.18681062400e11 -0.1762877569e10 / 0.1210809600e10; 0.56081e5 / 0.16473600e8 -0.634102039e9 / 0.65383718400e11 0.10259e5 / 0.4656960e7 0.278191e6 / 0.21525504e8 -0.84101639e8 / 0.13076743680e11 0.1469203e7 / 0.13759200e8 -0.1762877569e10 / 0.1210809600e10 0.10117212851e11 / 0.3736212480e10;];
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
75
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
76 M(1:8,1:8)=M_U;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
77
267
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
78 M(m-7:m,m-7:m)=rot90( M_U ,2 );
261
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
79 M=M/h;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
80
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
81 S_U=[-0.25e2 / 0.12e2 4 -3 0.4e1 / 0.3e1 -0.1e1 / 0.4e1;]/h;
267
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
82 S_1=sparse(1,m);
261
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
83 S_1(1:5)=S_U;
267
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
84 S_m=sparse(1,m);
261
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
85
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
86 S_m(m-4:m)=fliplr(-S_U);
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
87
267
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
88 D2=H\(-M-e_1*S_1+e_m*S_m);
261
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
89
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
90
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
91 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
92
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
93
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
94
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
95 % Third derivative, 1st order accurate at first 6 boundary points
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
96
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
97 q4=7/240;q3=-3/10;q2=169/120;q1=-61/30;
267
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
98 % Q3=q4*(diag(ones(m-4,1),4)-diag(ones(m-4,1),-4))+q3*(diag(ones(m-3,1),3)-diag(ones(m-3,1),-3))+q2*(diag(ones(m-2,1),2)-diag(ones(m-2,1),-2))+q1*(diag(ones(m-1,1),1)-diag(ones(m-1,1),-1));
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
99 diags = -4:4;
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
100 stencil = [-q4,-q3,-q2,-q1,0,q1,q2,q3,q4];
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
101 Q3 = stripeMatrix(stencil, diags, m);
261
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
102 %QQ3=(-1/8*diag(ones(m-3,1),3) + 1*diag(ones(m-2,1),2) - 13/8*diag(ones(m-1,1),1) +13/8*diag(ones(m-1,1),-1) -1*diag(ones(m-2,1),-2) + 1/8*diag(ones(m-3,1),-3));
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
103
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
104
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
105 Q3_U = [0 -0.10882810591e11 / 0.5811886080e10 0.398713069e9 / 0.132088320e9 -0.1746657571e10 / 0.1162377216e10 0.56050639e8 / 0.145297152e9 -0.11473393e8 / 0.1162377216e10 -0.38062741e8 / 0.1452971520e10 0.30473e5 / 0.4392960e7; 0.10882810591e11 / 0.5811886080e10 0 -0.3720544343e10 / 0.830269440e9 0.767707019e9 / 0.207567360e9 -0.1047978301e10 / 0.830269440e9 0.1240729e7 / 0.14826240e8 0.6807397e7 / 0.55351296e8 -0.50022767e8 / 0.1452971520e10; -0.398713069e9 / 0.132088320e9 0.3720544343e10 / 0.830269440e9 0 -0.2870078009e10 / 0.830269440e9 0.74962049e8 / 0.29652480e8 -0.12944857e8 / 0.30750720e8 -0.17846623e8 / 0.103783680e9 0.68707591e8 / 0.1162377216e10; 0.1746657571e10 / 0.1162377216e10 -0.767707019e9 / 0.207567360e9 0.2870078009e10 / 0.830269440e9 0 -0.727867087e9 / 0.276756480e9 0.327603877e9 / 0.207567360e9 -0.175223717e9 / 0.830269440e9 0.1353613e7 / 0.726485760e9; -0.56050639e8 / 0.145297152e9 0.1047978301e10 / 0.830269440e9 -0.74962049e8 / 0.29652480e8 0.727867087e9 / 0.276756480e9 0 -0.1804641793e10 / 0.830269440e9 0.311038417e9 / 0.207567360e9 -0.1932566239e10 / 0.5811886080e10; 0.11473393e8 / 0.1162377216e10 -0.1240729e7 / 0.14826240e8 0.12944857e8 / 0.30750720e8 -0.327603877e9 / 0.207567360e9 0.1804641793e10 / 0.830269440e9 0 -0.1760949511e10 / 0.830269440e9 0.2105883973e10 / 0.1452971520e10; 0.38062741e8 / 0.1452971520e10 -0.6807397e7 / 0.55351296e8 0.17846623e8 / 0.103783680e9 0.175223717e9 / 0.830269440e9 -0.311038417e9 / 0.207567360e9 0.1760949511e10 / 0.830269440e9 0 -0.1081094773e10 / 0.528353280e9; -0.30473e5 / 0.4392960e7 0.50022767e8 / 0.1452971520e10 -0.68707591e8 / 0.1162377216e10 -0.1353613e7 / 0.726485760e9 0.1932566239e10 / 0.5811886080e10 -0.2105883973e10 / 0.1452971520e10 0.1081094773e10 / 0.528353280e9 0;];
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
106
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
107 Q3(1:8,1:8)=Q3_U;
267
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
108 Q3(m-7:m,m-7:m)=rot90( -Q3_U ,2 );
261
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
109 Q3=Q3/h^2;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
110
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
111
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
112
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
113 S2_U=[0.35e2 / 0.12e2 -0.26e2 / 0.3e1 0.19e2 / 0.2e1 -0.14e2 / 0.3e1 0.11e2 / 0.12e2;]/h^2;
267
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
114 S2_1=sparse(1,m);
261
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
115 S2_1(1:5)=S2_U;
267
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
116 S2_m=sparse(1,m);
261
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
117 S2_m(m-4:m)=fliplr(S2_U);
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
118
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
119
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
120
267
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
121 D3=H\(Q3 - e_1*S2_1 + e_m*S2_m +1/2*(S_1'*S_1) -1/2*(S_m'*S_m) ) ;
261
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
122
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
123 % Fourth derivative, 0th order accurate at first 6 boundary points (still
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
124 % yield 4th order convergence if stable: for example u_tt=-u_xxxx
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
125
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
126 m4=7/240;m3=-2/5;m2=169/60;m1=-122/15;m0=91/8;
267
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
127 % M4=m4*(diag(ones(m-4,1),4)+diag(ones(m-4,1),-4))+m3*(diag(ones(m-3,1),3)+diag(ones(m-3,1),-3))+m2*(diag(ones(m-2,1),2)+diag(ones(m-2,1),-2))+m1*(diag(ones(m-1,1),1)+diag(ones(m-1,1),-1))+m0*diag(ones(m,1),0);
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
128 diags = -4:4;
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
129 left_stencil = [m4,m3,m2,m1];
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
130 stencil = [left_stencil,m0,fliplr(left_stencil)];
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
131 M4 = stripeMatrix(stencil, diags, m);
261
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
132 %M4=(-1/6*(diag(ones(m-3,1),3)+diag(ones(m-3,1),-3) ) + 2*(diag(ones(m-2,1),2)+diag(ones(m-2,1),-2)) -13/2*(diag(ones(m-1,1),1)+diag(ones(m-1,1),-1)) + 28/3*diag(ones(m,1),0));
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
133
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
134 M4_U=[0.40833734273e11 / 0.10761070320e11 -0.162181998421e12 / 0.16397821440e11 0.4696168417e10 / 0.521748864e9 -0.245714671483e12 / 0.68870850048e11 0.2185939219e10 / 0.2869618752e10 -0.15248255797e11 / 0.114784750080e12 0.345156907e9 / 0.12298366080e11 0.6388381e7 / 0.1093188096e10; -0.162181998421e12 / 0.16397821440e11 0.147281127041e12 / 0.5380535160e10 -0.3072614435609e13 / 0.114784750080e12 0.320122985851e12 / 0.28696187520e11 -0.768046031383e12 / 0.344354250240e12 0.7861605187e10 / 0.14348093760e11 -0.803762437e9 / 0.4251287040e10 0.167394281e9 / 0.86088562560e11; 0.4696168417e10 / 0.521748864e9 -0.3072614435609e13 / 0.114784750080e12 0.139712483333e12 / 0.4782697920e10 -0.1634124842747e13 / 0.114784750080e12 0.90855193447e11 / 0.28696187520e11 -0.26412188989e11 / 0.38261583360e11 0.668741173e9 / 0.1793511720e10 -0.132673781e9 / 0.2342545920e10; -0.245714671483e12 / 0.68870850048e11 0.320122985851e12 / 0.28696187520e11 -0.1634124842747e13 / 0.114784750080e12 0.437353997177e12 / 0.43044281280e11 -0.172873969321e12 / 0.38261583360e11 0.34759553483e11 / 0.28696187520e11 -0.98928859751e11 / 0.344354250240e12 0.295000207e9 / 0.3587023440e10; 0.2185939219e10 / 0.2869618752e10 -0.768046031383e12 / 0.344354250240e12 0.90855193447e11 / 0.28696187520e11 -0.172873969321e12 / 0.38261583360e11 0.126711914423e12 / 0.21522140640e11 -0.520477408939e12 / 0.114784750080e12 0.49581230003e11 / 0.28696187520e11 -0.99640101991e11 / 0.344354250240e12; -0.15248255797e11 / 0.114784750080e12 0.7861605187e10 / 0.14348093760e11 -0.26412188989e11 / 0.38261583360e11 0.34759553483e11 / 0.28696187520e11 -0.520477408939e12 / 0.114784750080e12 0.19422074929e11 / 0.2391348960e10 -0.772894368601e12 / 0.114784750080e12 0.10579712849e11 / 0.4099455360e10; 0.345156907e9 / 0.12298366080e11 -0.803762437e9 / 0.4251287040e10 0.668741173e9 / 0.1793511720e10 -0.98928859751e11 / 0.344354250240e12 0.49581230003e11 / 0.28696187520e11 -0.772894368601e12 / 0.114784750080e12 0.456715296239e12 / 0.43044281280e11 -0.915425403107e12 / 0.114784750080e12; 0.6388381e7 / 0.1093188096e10 0.167394281e9 / 0.86088562560e11 -0.132673781e9 / 0.2342545920e10 0.295000207e9 / 0.3587023440e10 -0.99640101991e11 / 0.344354250240e12 0.10579712849e11 / 0.4099455360e10 -0.915425403107e12 / 0.114784750080e12 0.488029542379e12 / 0.43044281280e11;];
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
135
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
136 M4(1:8,1:8)=M4_U;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
137
267
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
138 M4(m-7:m,m-7:m)=rot90( M4_U ,2 );
261
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
139 M4=M4/h^3;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
140
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
141 S3_U=[-0.5e1 / 0.2e1 9 -12 7 -0.3e1 / 0.2e1;]/h^3;
267
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
142 S3_1=sparse(1,m);
261
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
143 S3_1(1:5)=S3_U;
267
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
144 S3_m=sparse(1,m);
261
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
145 S3_m(m-4:m)=fliplr(-S3_U);
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
146
267
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
147 D4=H\(M4-e_1*S3_1+e_m*S3_m + S_1'*S2_1-S_m'*S2_m);
261
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
148
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
149
267
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
150 % L=h*(m-1);
261
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
151
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
152 % x1=linspace(0,L,m)';
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
153 % x2=x1.^2/fac(2);
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
154 % x3=x1.^3/fac(3);
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
155 % x4=x1.^4/fac(4);
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
156 % x5=x1.^5/fac(5);
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
157
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
158 % x0=x1.^0/fac(1);
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
159
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
160 S_1 = S_1';
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
161 S2_1 = S2_1';
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
162 S3_1 = S3_1';
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
163 S_m = S_m';
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
164 S2_m = S2_m';
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
165 S3_m = S3_m';
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
166
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
167
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
168 end